{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import math\n",
    "from sklearn.model_selection import train_test_split\n",
    "from data import *\n",
    "from evaluation import *\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 加载数据集"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " data length: 100000 \n",
      " user number: 943 \n",
      " item number: 1682\n"
     ]
    }
   ],
   "source": [
    "data_dir = 'datasets/ml-100k/u.data' \n",
    "N, M, data_list, _ = load_data(file_dir=data_dir)\n",
    "print(' data length: %d \\n user number: %d \\n item number: %d' %(len(data_list),N,M))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 分割数据集"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "train length: 80000 \n",
      " test length: 20000\n"
     ]
    }
   ],
   "source": [
    "train_list, test_list = train_test_split(data_list,test_size=0.2)\n",
    "print ('train length: %d \\n test length: %d' %(len(train_list),len(test_list)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 将 list 转换成 矩阵"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train_mat = sequence2mat(sequence = train_list, N = N, M = M)\n",
    "test_mat = sequence2mat(sequence = test_list, N = N, M = M)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 参数设置"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "users_num = N            #用户数\n",
    "items_num = M            #商品数\n",
    "hidden_size = 500        #隐层节点数目，即用户的嵌入空间维度\n",
    "batch_size = 256         #batch大小\n",
    "lamda_regularizer = 1e-3 #正则项系数\n",
    "learning_rate = 1e-3  #学习率\n",
    "epoches  = 100\n",
    "embedding_size = 8"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. MLP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch:0  loss=13.8889; \n",
      " MAE=3.4817; RMSE=3.6595; Recall=0.0163; Precision=0.0346; Hit=0.0163; NDCG=0.0071\n",
      "epoch:10  loss=1.3124; \n",
      " MAE=0.8106; RMSE=1.0135; Recall=0.0547; Precision=0.1160; Hit=0.0547; NDCG=0.0277\n",
      "epoch:20  loss=1.0300; \n",
      " MAE=0.7608; RMSE=0.9597; Recall=0.0435; Precision=0.0924; Hit=0.0435; NDCG=0.0196\n",
      "epoch:30  loss=0.7246; \n",
      " MAE=0.7514; RMSE=0.9500; Recall=0.0374; Precision=0.0792; Hit=0.0374; NDCG=0.0163\n",
      "epoch:40  loss=0.9613; \n",
      " MAE=0.7498; RMSE=0.9474; Recall=0.0362; Precision=0.0767; Hit=0.0362; NDCG=0.0158\n",
      "epoch:50  loss=0.8649; \n",
      " MAE=0.7477; RMSE=0.9462; Recall=0.0327; Precision=0.0694; Hit=0.0327; NDCG=0.0146\n",
      "epoch:60  loss=1.0315; \n",
      " MAE=0.7472; RMSE=0.9458; Recall=0.0328; Precision=0.0695; Hit=0.0328; NDCG=0.0146\n",
      "epoch:70  loss=1.2084; \n",
      " MAE=0.7473; RMSE=0.9456; Recall=0.0301; Precision=0.0637; Hit=0.0301; NDCG=0.0137\n",
      "epoch:80  loss=1.0308; \n",
      " MAE=0.7456; RMSE=0.9456; Recall=0.0279; Precision=0.0593; Hit=0.0279; NDCG=0.0128\n",
      "epoch:90  loss=0.7231; \n",
      " MAE=0.7475; RMSE=0.9455; Recall=0.0269; Precision=0.0571; Hit=0.0269; NDCG=0.0123\n"
     ]
    },
    {
     "data": {
      "image/png": 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IHkBf4HM8g0gd8Ji3/FXgYufcw2bWGHgBaAZ8DRznnMuvzslaNW4VULYhd4OCh4iISITV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\nRjwAgI14AACbAJIgAaIJp2FgAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1209e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Llo3rQAvnLKRjWge7+3fvaXtg0wMGEUnSPq/eL+dr1qxh+fLlLTnehAgiETEX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\nu1Z01AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x102d74a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ostmq434dx54Te9xiBZ1Ym13l6Mpc0eAKt9ids+7kzWVvkpGZcU45ioiIFDdBL1aAqkA4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\nHvgEcCywG3AlcEGSbQe0Xwh8HfgWsAg4GTg9yct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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a5c9dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mlp import *\n",
    "learning_rate = 1e-4  #学习率\n",
    "hidden_sizes = [embedding_size,int(embedding_size/2)]\n",
    "model = mlp(users_num = users_num,\n",
    "            items_num = items_num,\n",
    "            embedding_size = embedding_size,\n",
    "            hidden_sizes = hidden_sizes,\n",
    "            learning_rate = learning_rate,\n",
    "            lamda_regularizer = lamda_regularizer,\n",
    "            batch_size = batch_size)\n",
    "\n",
    "records_list = []\n",
    "input_data = train_list\n",
    "for epoch in range(epoches):\n",
    "    data_mat = np.random.permutation(input_data) \n",
    "    loss = model.train(data_sequence=data_mat)\n",
    "    pred_mat = model.predict_ratings(data_sequence=test_list)\n",
    "    mae, rmse, recall, precision = evaluation(pred_mat, train_mat, test_mat)\n",
    "    records_list.append([loss[-1],mae, rmse, recall, precision])\n",
    "    if epoch % 10==0:\n",
    "        topn = get_topn(pred_mat, train_mat, n=10)\n",
    "        hit_list, ndcg_list = hit_ndcg(test_sequence=np.array(test_list), ranklist=topn)\n",
    "        hit, ndcg = np.array(hit_list).mean(),np.array(ndcg_list).mean()\n",
    "        print('epoch:%d  loss=%.4f; \\n MAE=%.4f; RMSE=%.4f; Recall=%.4f; Precision=%.4f; Hit=%.4f; NDCG=%.4f'\n",
    "              %(epoch, loss[-1], mae, rmse, recall, precision, hit, ndcg))\n",
    "\n",
    "figure(values_list=np.array(records_list)[:,0],name='loss')\n",
    "figure(values_list=np.array(records_list)[:,2],name='RMSE')\n",
    "figure(values_list=np.array(records_list)[:,-1],name='Precision')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. AutoRec\n",
    "- 基于用户的 autorec 模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch:0  loss=18.7725; \n",
      " MAE=2.5896; RMSE=2.9917; Recall=0.0107; Precision=0.0228\n",
      "epoch:10  loss=7.6541; \n",
      " MAE=0.9232; RMSE=1.1557; Recall=0.0167; Precision=0.0354\n",
      "epoch:20  loss=5.7720; \n",
      " MAE=0.8840; RMSE=1.1059; Recall=0.0225; Precision=0.0476\n",
      "epoch:30  loss=4.4838; \n",
      " MAE=0.8712; RMSE=1.0888; Recall=0.0242; Precision=0.0513\n",
      "epoch:40  loss=3.4905; \n",
      " MAE=0.8622; RMSE=1.0760; Recall=0.0275; Precision=0.0583\n",
      "epoch:50  loss=2.8091; \n",
      " MAE=0.8543; RMSE=1.0656; Recall=0.0291; Precision=0.0618\n",
      "epoch:60  loss=2.3000; \n",
      " MAE=0.8487; RMSE=1.0574; Recall=0.0310; Precision=0.0657\n",
      "epoch:70  loss=1.9391; \n",
      " MAE=0.8451; RMSE=1.0520; Recall=0.0324; Precision=0.0688\n",
      "epoch:80  loss=1.6394; \n",
      " MAE=0.8417; RMSE=1.0468; Recall=0.0335; Precision=0.0709\n",
      "epoch:90  loss=1.3985; \n",
      " MAE=0.8389; RMSE=1.0430; Recall=0.0336; Precision=0.0714\n"
     ]
    },
    {
     "data": {
      "image/png": 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zkZ6GKyISJhQ8JOiOHHQky69ezt0n301an7Rm++0q3sW9X9zLMf86hvT70rn3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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x185e9da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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FEQerSpLUOIoXRLyzqiRJDaNwQcT7iEiS1DgKF0S8s6okSY2jcEHEp+9KktQ4ChdExhus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\npNwYRCRJUm4MIpIkKTcGEUmSlJv/D50CZauDE6UCAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x102cfeb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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oSuY+vLj6RTrU6kDLai1Zd3gdC/5aYLnmkfaPuPziplROabLiQ1klK5npyIpS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\n3P0d1m1YN6rs+AOOH0jbJEkaBsNKH+s3rufpZ58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2M6xIkqRWM6xIkqRWM6xIkqRWM6xI\nkqRWM6xIkqRWM6xIkqRWM6xIkqRWM6xI2qYluTPJKU23Q9LgGFYkTVqSLyT5av3vbyc5a4jvfVK9\nt0i3w4H/Pax2SBo+NzKU1Kgks0q1+/mEVYEx+4OUUh6Z/lZJahNHViRNWZIvUG1w9qEkm5NsSvLC\n+tjLknwjyeNJHkjypSR7dJz77SR/leTsJA8B/1qXfyTJ9UmeSHJ3knOS7FofOwo4D5jf8X7/oz42\nahooyT5Jvla//9okf5/k+R3HP5Hk2iQn1ueuSbKq3l12pM5b6rasT/JwkkuS7DLQTpXUl2FF0pY4\nhWp38r8BFgF7AfckmQ98E7gGeAVwHPB84IKu898BbABeA7ynLtsEfBB4aX38V4E/r499D/gwsK7j\n/f6iu1FJAlwELACOBI4FXgR8pavq/sBvUe2SfAJV8Dqtfo3FwN8B5wIH18e+SjWyI6kBTgNJmrJS\nyuNJngHWl1IeGilP8gFgdSnljI6y5cDdSV5cSrm9Lr6tlHJa12uu6Hh6d5IzgM8BHyilbEyytqr2\n8/fr4VjgPwNLSin31e//DuCGJEtLKdeMNAs4qZSyvq5zPnAMcAZVEJoJ/FMp5Z66/g2T7RtJ08+R\nFUnT6RDg6HoK5vEkjwM3Ua012b+j3jXdJyY5NsmlSe5Nsg44H9gjyZwpvP/BwD0jQQWglHITsAZ4\nSUe9u0aCSu1+qhEggOuoRod+nOSCJMuTLJhCGyRNM8OKpOk0l2oa5uVUwWXkcQBweUe9JztPSrIv\n8HXgR8DvUE0hvb8+vPMA2tm9oLdQ/z4spWwupbwB+DWqEZUPAjfXbZTUAMOKpC31DNV0SafVVNMw\nPy2l3NH1eGqc11oKpJTy8VLKVfV00X+axPt1uwnYJ8lz5yZ5KdUalilN5ZRSriylfBI4jCrcvGkq\n50uaPoYVSVvqLuBVSfbtuNrnHGAh8JUkhyd5UZLjkpxXL37t53ZgVpJTkuyX5PeBd/d4v7lJjk6y\nR6+rc0oplwI/Br6c5LAkrwT+D/DtUsq1k/mikrwyyelJlibZB3gzsCdw42TOlzT9DCuSttRfUF3B\ncyPwH0leWEq5H3gt1e+Wi4HrgbOAx0opI/dI6XWvlOuBjwKnAv8OLKO+OqejzpXA54G/B/4D+K99\nXu+NwGPAZcAlVEHo7VP4utYBvwL8P+AW4Ezgo6WUS6bwGpKmUX7++0OSJKl9HFmRJEmtZliRJEmt\nZliRJEmtZliRJEmtZliRJEmtZliRJEmtZliRJEmtZliRJEmtZliRJEmtZliRJEmtZliRJEmtZliR\nJEmt9v8BWinmj6AogiEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c07e438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from autorec import *\n",
    "model = autorec(users_num = users_num,\n",
    "                items_num = items_num,\n",
    "                hidden_size = hidden_size,\n",
    "                batch_size = batch_size,\n",
    "                learning_rate = learning_rate,\n",
    "                lamda_regularizer = lamda_regularizer)\n",
    "\n",
    "records_list = []\n",
    "for epoch in range(epoches):\n",
    "    data_mat = np.random.permutation(train_mat) \n",
    "    loss = model.train(data_mat=data_mat)\n",
    "    pred_mat = model.predict_ratings(data_mat=train_mat)\n",
    "    mae, rmse, recall, precision = evaluation(pred_mat, train_mat, test_mat)\n",
    "    records_list.append([loss[-1],mae, rmse, recall, precision])\n",
    "    if epoch % 10==0:\n",
    "        print('epoch:%d  loss=%.4f; \\n MAE=%.4f; RMSE=%.4f; Recall=%.4f; Precision=%.4f'\n",
    "              %(epoch, loss[-1], mae, rmse, recall, precision))\n",
    "\n",
    "figure(values_list=np.array(records_list)[:,0],name='loss')\n",
    "figure(values_list=np.array(records_list)[:,2],name='RMSE')\n",
    "figure(values_list=np.array(records_list)[:,-1],name='Precision')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### AutoRec\n",
    "- 基于商品的 autorec 模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch:0  loss=10.4750; \n",
      " MAE=1.8537; RMSE=5.0995; Recall=0.0240; Precision=0.0510\n",
      "epoch:10  loss=4.5704; \n",
      " MAE=0.8406; RMSE=1.1229; Recall=0.0273; Precision=0.0580\n",
      "epoch:20  loss=3.4024; \n",
      " MAE=0.8137; RMSE=1.0517; Recall=0.0336; Precision=0.0713\n",
      "epoch:30  loss=2.5409; \n",
      " MAE=0.7993; RMSE=1.0148; Recall=0.0410; Precision=0.0870\n",
      "epoch:40  loss=1.9396; \n",
      " MAE=0.7904; RMSE=0.9919; Recall=0.0474; Precision=0.1006\n",
      "epoch:50  loss=1.5310; \n",
      " MAE=0.7860; RMSE=0.9788; Recall=0.0541; Precision=0.1147\n",
      "epoch:60  loss=1.2439; \n",
      " MAE=0.7838; RMSE=0.9716; Recall=0.0573; Precision=0.1215\n",
      "epoch:70  loss=1.0478; \n",
      " MAE=0.7802; RMSE=0.9635; Recall=0.0595; Precision=0.1261\n",
      "epoch:80  loss=0.9138; \n",
      " MAE=0.7777; RMSE=0.9584; Recall=0.0610; Precision=0.1294\n",
      "epoch:90  loss=0.7975; \n",
      " MAE=0.7777; RMSE=0.9577; Recall=0.0639; Precision=0.1355\n"
     ]
    },
    {
     "data": {
      "image/png": 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NPjNWzGDoQ0OZvmC6Jp+KiEi9KXhInSIsgvQj0/nu6u+48MgLa2zfuW8nV751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\nmlkxsM85t2N/u5ldCyx0zv2xUtvlwEY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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b938048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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URM3rw4DOPewzLzrbZ17WlgpJkoo1H2Mq0jyccyfdHTUtFQ7UlCSpUE07ULOzzZYKSZIa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\nC0OFJEnKhaFCkiTlwlAhSZJy8f8Dc5RnQIcpviMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1bbbeb00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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bho0HNvrE7zjvDgacOyA4SYlInlKxIiIFxrhfx9F5bGf2Ht/rE29Xqx3Duw4P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\n0L6jmS0xsxNm9oeZDfTTppyZvWNm273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0XKGngGOA2cBk57uh+b4SuH8zMc57sTm/C/hx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\nMyu1/wGfehFls8SU0wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c47ff60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = autorec(users_num = items_num,\n",
    "                items_num = users_num,\n",
    "                hidden_size = hidden_size,\n",
    "                batch_size = batch_size,\n",
    "                learning_rate = learning_rate,\n",
    "                lamda_regularizer = lamda_regularizer)\n",
    "\n",
    "records_list = []\n",
    "for epoch in range(epoches):\n",
    "    data_mat = np.random.permutation(train_mat.T) \n",
    "    loss = model.train(data_mat=data_mat)\n",
    "    pred_mat = model.predict_ratings(data_mat=train_mat.T)\n",
    "    mae, rmse, recall, precision = evaluation(pred_mat.T, train_mat, test_mat)\n",
    "    records_list.append([loss[-1],mae, rmse, recall, precision])\n",
    "    if epoch % 10==0:\n",
    "        print('epoch:%d  loss=%.4f; \\n MAE=%.4f; RMSE=%.4f; Recall=%.4f; Precision=%.4f'\n",
    "              %(epoch, loss[-1], mae, rmse, recall, precision))\n",
    "\n",
    "figure(values_list=np.array(records_list)[:,0],name='loss')\n",
    "figure(values_list=np.array(records_list)[:,2],name='RMSE')\n",
    "figure(values_list=np.array(records_list)[:,-1],name='Precision')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5. CDAE\n",
    "- 基于用户"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch:0  loss=49.5955; \n",
      " MAE=2.1029; RMSE=5.6706; Recall=0.0145; Precision=0.0308\n",
      "epoch:10  loss=10.1589; \n",
      " MAE=2.6123; RMSE=8.3518; Recall=0.0491; Precision=0.1042\n",
      "epoch:20  loss=9.4686; \n",
      " MAE=2.9019; RMSE=10.0385; Recall=0.0485; Precision=0.1029\n",
      "epoch:30  loss=8.8841; \n",
      " MAE=2.9282; RMSE=10.2211; Recall=0.0488; Precision=0.1036\n",
      "epoch:40  loss=8.9273; \n",
      " MAE=2.9155; RMSE=10.1267; Recall=0.0508; Precision=0.1076\n",
      "epoch:50  loss=9.5272; \n",
      " MAE=2.9096; RMSE=10.0948; Recall=0.0529; Precision=0.1121\n",
      "epoch:60  loss=8.5919; \n",
      " MAE=2.9076; RMSE=10.0903; Recall=0.0491; Precision=0.1042\n",
      "epoch:70  loss=8.7455; \n",
      " MAE=2.9200; RMSE=10.1678; Recall=0.0549; Precision=0.1164\n",
      "epoch:80  loss=8.5345; \n",
      " MAE=2.9143; RMSE=10.1181; Recall=0.0514; Precision=0.1090\n",
      "epoch:90  loss=9.1166; \n",
      " MAE=2.9105; RMSE=10.1240; Recall=0.0494; Precision=0.1048\n"
     ]
    },
    {
     "data": {
      "image/png": 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b3dfXd9/NUpuxi+96OdTjISIiEq7Qh1rKM7MUM7sMaAlMLbfpFDNbZ2YLzOwhM2tXl/01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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x15fdb3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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CggkLuGreVSw9bikjCkYQcAE6Ah10BDrIzc6N+YWmobWBTTWb2Fi9kcc2P8b9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\neMzBchYbcFIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1088f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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gRV2+zLVW/ONvvoqDWdNAB84c0EYSnKcBR7WRg5Udp3a4rHM0bcM06VrR4dG4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\n2JO1B7ZyG2ZumSmde33n6wP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wCNzZ/U7s/ttu/GvQvxAXKffF3bREMLRPbe/xwymMwvye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\nJGmo/T/OnnqDINytmgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x19fcf6d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from cdae import *\n",
    "hidden_size = 50        #隐层节点数目，即用户的嵌入空间维度\n",
    "lamda_regularizer = 1e-2 #正则项系数\n",
    "learning_rate = 0.01  #学习率\n",
    "dropout_rate = 0.5        # dropout rate \n",
    "model = cdae(users_num = users_num,\n",
    "             items_num = items_num,\n",
    "             hidden_size = hidden_size,\n",
    "             batch_size = batch_size,\n",
    "             learning_rate = learning_rate,\n",
    "             lamda_regularizer = lamda_regularizer,\n",
    "             dropout_rate = dropout_rate)\n",
    "\n",
    "user_array = np.array([u for u in range(users_num)])\n",
    "input_data = np.c_[user_array, train_mat]\n",
    "records_list = []\n",
    "for epoch in range(epoches):\n",
    "    data_mat = np.random.permutation(input_data) \n",
    "    loss = model.train(data_mat=data_mat)\n",
    "    pred_mat = model.predict_ratings(data_mat=np.c_[user_array, train_mat])\n",
    "    mae, rmse, recall, precision = evaluation(pred_mat, train_mat, test_mat)\n",
    "    records_list.append([loss[-1],mae, rmse, recall, precision])\n",
    "    if epoch % 10==0:\n",
    "        print('epoch:%d  loss=%.4f; \\n MAE=%.4f; RMSE=%.4f; Recall=%.4f; Precision=%.4f'\n",
    "              %(epoch, loss[-1], mae, rmse, recall, precision))\n",
    "\n",
    "figure(values_list=np.array(records_list)[:,0],name='loss')\n",
    "figure(values_list=np.array(records_list)[:,2],name='RMSE')\n",
    "figure(values_list=np.array(records_list)[:,-1],name='Precision')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "- 基于商品"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch:0  loss=30.7612; \n",
      " MAE=1.1538; RMSE=2.0037; Recall=0.0242; Precision=0.0512\n",
      "epoch:10  loss=8.8757; \n",
      " MAE=2.9567; RMSE=10.1285; Recall=0.0694; Precision=0.1472\n",
      "epoch:20  loss=8.3818; \n",
      " MAE=2.9470; RMSE=10.0405; Recall=0.0704; Precision=0.1494\n",
      "epoch:30  loss=8.4252; \n",
      " MAE=2.9705; RMSE=10.1892; Recall=0.0679; Precision=0.1441\n",
      "epoch:40  loss=8.5532; \n",
      " MAE=2.9684; RMSE=10.1922; Recall=0.0740; Precision=0.1568\n",
      "epoch:50  loss=8.5284; \n",
      " MAE=2.9607; RMSE=10.1337; Recall=0.0736; Precision=0.1562\n",
      "epoch:60  loss=8.3302; \n",
      " MAE=2.9018; RMSE=9.7697; Recall=0.0636; Precision=0.1350\n",
      "epoch:70  loss=8.3040; \n",
      " MAE=2.8864; RMSE=9.6533; Recall=0.0664; Precision=0.1407\n",
      "epoch:80  loss=8.3288; \n",
      " MAE=2.9436; RMSE=10.0288; Recall=0.0671; Precision=0.1423\n",
      "epoch:90  loss=8.2134; \n",
      " MAE=2.9342; RMSE=9.9701; Recall=0.0684; Precision=0.1451\n"
     ]
    },
    {
     "data": {
      "image/png": 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DE0xFRETCL3aCh0otIiIiYRczwUOlFhERkfCLmeChUouIiEj4xU7wUKlFREQk7GImeKjU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\nMarbKMYPGF/oZLvtB7aTvC2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l0V82vs8oHfPyV8JjvADIzLNOB7xQ/n1J9xWNpZYngTfM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\nPcE3zDjuAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a242b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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D84B2Pg+1BdaW9nx+xaXFZTyylfEQEREJp4jIeJhZInAkUDCj5XAz6wLscM6tBx4H3jGz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\noAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b68bf60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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QsQIh+6iJWDFp23Zkm2H5j/3164Ixs6xsOFx/RmKz7wkwFys3fnkjTnvrNAx+YzD+/eO/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\nkjTQDCuSJGmg/X9o/Y/FXlZW3AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b9b4cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = cdae(users_num = items_num,\n",
    "             items_num = users_num,\n",
    "             hidden_size = hidden_size,\n",
    "             batch_size = batch_size,\n",
    "             learning_rate = learning_rate,\n",
    "             lamda_regularizer = lamda_regularizer,\n",
    "             dropout_rate = dropout_rate)\n",
    "\n",
    "item_array = np.array([i for i in range(items_num)])\n",
    "input_data = np.c_[item_array, train_mat.T]\n",
    "records_list = []\n",
    "for epoch in range(epoches):\n",
    "    data_mat = np.random.permutation(input_data) \n",
    "    loss = model.train(data_mat=data_mat)\n",
    "    pred_mat = model.predict_ratings(data_mat=np.c_[item_array, train_mat.T])\n",
    "    mae, rmse, recall, precision = evaluation(pred_mat.T, train_mat, test_mat)\n",
    "    records_list.append([loss[-1],mae, rmse, recall, precision])\n",
    "    if epoch % 10==0:\n",
    "        print('epoch:%d  loss=%.4f; \\n MAE=%.4f; RMSE=%.4f; Recall=%.4f; Precision=%.4f'\n",
    "              %(epoch, loss[-1], mae, rmse, recall, precision))\n",
    "\n",
    "figure(values_list=np.array(records_list)[:,0],name='loss')\n",
    "figure(values_list=np.array(records_list)[:,2],name='RMSE')\n",
    "figure(values_list=np.array(records_list)[:,-1],name='Precision')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [default]",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
